Assume a constant state of falling rain, coming straight down.  Your
car is 50 yards from the restaurant door.  Do you get more wet
walking, running at twice the speed of walking, or is it the same due
to some sort of compression effect?

In this case scientific analysis agrees with the common sense:
 
 Amount of water objects collects is proportional to the time 
 spent in the rain

The formula

"..

RC = D * T * v  * x / s    +  5 * D * T * x  .."

is derived e.g.  here

http://www.madsci.org/posts/archives/1997-12/875637984.Ph.r.html

 In that formula
                       t = x / s  = distance over speed is 
 time spent in the rain.

This is true even if rain is not vertical:

http://www.madsci.org/posts/archives/mar2001/985815156.Ph.r.html

or if you draw a picture during the analysis: 

http://www.madsci.org/posts/archives/2004-01/1074093706.Es.r.html

 This is a FAQ on the high school science circuit, probably stemming from
a related question, namely:
                           Amount of rain hitting the windshield
discussed e.g. here:
http://www.newton.dep.anl.gov/newton/askasci/1995/environ/ENV022.HTM

  In the original question, teacher was asking:

 During the SAME TIME interval, is the amount of water collected,
 different for a moving car than for a stationary car?

 The angle of drops relative to car is different when car is
moving - and there is an effect, which can be called a compression effect,
which compensates for that - a different effective crossection of the exposed area.
 These two effects cancel each other, so that

  The rate of wetting is same, 


and so, in summary:
 the longer you run, walk or dance in the rain
the wetter you will become.

 However, The "angle of incidence"  of rain drops changes with the speed
 of the body.
 That angle is shown here:

http://scienceworld.wolfram.com/physics/AngleofIncidence.html

Hedgie

"and so, in summary: the longer you run, walk or dance in the rain the
wetter you will become."

<smile>  well, I'm always impressed by the scientific method . . .

I live in the Pacific North Wet and I coulda told ya this for fifty cents . . .   :)

Most important is which way the wind is blowing!

It is not true that the rate of wetting is independent of your speed. 
You get wetter quicker when you move faster.  I know this from
experience (riding a motorcycle in the rain), but you can also see it
from common sense.  Go into the reference frame of the falling
raindrops.  That is, look at the world as if you're a raindrop.  All
the raindrops are motionless in this reference frame (all raindrops
are assumed to have the same terminal velocity), and objects which are
stationary relative to the groud are moving upward through the
raindrops.  The amount of wetting that occurs is equal to the number
of raindrops the object hits.  So if the rain is falling vertically at
3 m/s, it will 'see' a sphere sitting on the ground as moving at 3
m/s, but it will 'see' a sphere rolling across the horizontal ground
at 4 m/s as moving at 5 m/s.  So the moving sphere will get wet 1.6
times faster than the stationary one.
As for whether you should walk or run from your car to the restaurant,
that depends.  If both your walking speed and running speed are much
larger than the speed of the falling rain (as would be the case if the
'rain' were a fine mist or drizzle that settled slowly), then it
doesn't matter.  In moving from your car to the resaurant you sweep
out a given volume which contains a given number of drops.  When you
run you get wet twice as fast for half as long, and the end result is
the same.  If you are spherical, and the speed of the rain is
reasonably large, then you will get less wet if you run.  But most
people are taller and skinnier than spheres.  So when you're standing
still, the vertically falling rain sees a much smaller target than
when you're moving forward.  The faster you move, the more
perpendicularly the rain hits you, and so the bigger the target for
the rain.  In the limit of an extremely tall and skinny person, once
again it doesn't matter whether you walk or run.  You'll get equally
wet either way.

This first thing to clarify is that, when asking this standard
question, we are really imagining a situation such as running from a
car to a house in the rain.  There is logic in saying a running person
runs into more rain, but we aren't running around in the rain in
circles like idiots, we are trying to get from one specific point to
another.  A running person might "run into" more rain per second than
a person walking or standing still, but until you get from your car to
your house you are still getting rained on.

Imagine the rain is hovering in the air.  For a fixed distance of
travel, the front of your body would have to push through the same
total area of air/rain.  Speed wouldn't matter.

Now if the rain is falling at a constant speed, it still wouldn't make
a difference to the front of your body what speed you were moving--you
would still have to move through the same volume of air which has a
constant mix of water in it.  But while you are standing there
thinking about how much rain the front of your body runs into, the top
of your head is getting rained on.  The rain falling on the top of
your head will run down the rest of you too, so hurry up and get
inside.

But instead of trying to prove it, if someone tells you that going
slower means getting rained on less, or the same amount, ask them why
they don't just stand still in the rain and not move at all.  Put the
burden on them to determine exactly how slow they think they should
move in the rain.  That ought to make it seem ridiculous enough.

xcarlx-

Your comment says the same thing as mine in different words.

racecar said:
> xcarlx-
>
> Your comment says the same thing as mine in different words.

Oops.  Had I read more carefully, I wouldn't have wasted all those words.

Sorry to bring this back up, but I was biking in the rain today and
thought of this...  The slower you go (as speed approaches 0) the
number of raindrops that hit you goes to infinity.  However, the
faster you go (as speed approaches infinity) the number of raindrops
doesn't go to infinity.

Since we're assuming there's a finite number of drops at any one
moment in the air, then wouldn't there be a cap on the number of drops
you can hit, even if you hit them all?  Then wouldn't that result in
the faster you go, the less wet you'd get?

Xiao